Question

sides of angle pqr and angle xyz are parallel to each other prove that pqr = angle xyz​

Answer 1

Appropriate Question :-

sides of angle PQR and angle XYZ are parallel to each other prove that ∆PQR = angle ∆XYZ.

Solution :-

Here,

$\rm:\longmapsto{PQ \parallel XY \: and \: PQ = XY } \\ \\ \rm :\longmapsto{PR \parallel X Z \: and \:PR = X Z } \:$

Taking $\triangle$ PQR and $\triangle$ XYZ

PQ = XY

PR = XZ

$\rm :\longmapsto{ \angle QPX = \angle YXM = a} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \rm : \longmapsto{ \angle RPX = \angle ZXM = b} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \rm : \longmapsto{ \angle XYZ = \angle YXM + \angle ZXM = a + b} \\ \\ \rm : \longmapsto{\angle XYZ = \angle PQR = a + b} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Hence,

$\rm:\longmapsto \red{\triangle PQR \cong \triangle XYZ }$

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Answer 2

Answer:

line Z and R is parallel to each other.

so angleY = angle1 ( corresponding angles )

Then ,

P and X is parallel to each other.

so , angle1 = angle2 ( corresponding angles )

angle2 is angleQ

so angleY=angleQ ( hence proved )

I hope it will helpful.